Y=45-(9n+7)n=2

Solution for Y=45-(9n+7)n=2 equation:

=45-(9Y+7)Y=2

We move all terms to the left:

-(45-(9Y+7)Y)=0


We calculate terms in parentheses: -(45-(9Y+7)Y), so:

45-(9Y+7)Y

determiningTheFunctionDomain
-(9Y+7)Y+45

We multiply parentheses

-9Y^2-7Y+45

Back to the equation:

-(-9Y^2-7Y+45)


We get rid of parentheses

9Y^2+7Y-45=0

a = 9; b = 7; c = -45;
Δ = b2-4ac
Δ = 72-4·9·(-45)
Δ = 1669
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{1669}}{2*9}=\frac{-7-\sqrt{1669}}{18}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{1669}}{2*9}=\frac{-7+\sqrt{1669}}{18}
$